• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.527-535
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• 2011

This study proposes a modified definition about $C_{pk}$ based on median as the centering parameter in order to more easily control the process since the mean does not represent any quantile of the asymmetric process distribution. Then we consider an estimate and derive the asymptotic normality for the estimate of the modified $C_{pk}$. In addition, we provide an example with asymmetric distributions and discuss the estimation for the limiting variance that are followed by some concluding remarks.

• International Journal of Reliability and Applications
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• v.16 no.2
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• pp.123-133
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• 2015

In this paper, the problem of testing exponentiality against net decreasing variance residual lifetime (NDVRL) classes of life distributions is investigated. For this property a nonparametric test is presented based on kernel method. The test is presented for complete and right censored data. Furthermore, Pitman's asymptotic relative efficiency (PARE) is discussed to assess the performance of the test with respect to other tests. Selected critical values are tabulated. Some numerical simulations on the power estimates are presented for proposed test. Finally, numerical examples are presented for the purpose of illustrating our test.

• Journal of the Korean Data and Information Science Society
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• v.6 no.2
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• pp.65-76
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• 1995

The importance of left truncated and right censoring cases has considered for better information in medical follow-up and engineering life testing studies. We propose some estimation procedure for the mean residual life function with consistency and asymptotic normality on the left truncated and right censoring model. And then, the comparision with Kaplan-Meier estimator ignoring the left truncated effect and the small sample properities are investigated by asymptotic biases and M.S.E.'s thresh Monte Carlo study.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.537-547
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• 2011

In this article, we propose an estimation procedure for the treatment eect for the right censored data. We apply the least square method for deriving the estimation equation and obtain an explicit formula for an estimation. Then we consider some asymptotic properties with derivation of the asymptotic normality for the estimate. Finally we illustrate our procedure with an example and discuss some interesting aspects for the estimation procedure.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.933-943
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• 2008

Spectral analysis of a strictly stationary r-vector valued time series is considered under the assumption that some of the observations are missed due to some random failure. Statistical properties and asymptotic moments are derived. Asymptotic normality is discussed.

• International Journal of Reliability and Applications
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• v.10 no.2
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• pp.81-88
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• 2009

A non-parametric procedure is presented for testing exponentially against used better than aged in convex ordering class (UBAC) of life distributions based on u-test. Convergence of the proposed statistic to the normal distribution is proved. Selected critical values are tabulated for sample sizes 5(5)40. The Pitman asymptotic relative efficiency of my proposed test to tests of other classes is studied. An example of 40 patients suffering from blood cancer disease demonstrates practical application of the proposed test.

• Journal of the Korean Statistical Society
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• v.26 no.3
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• pp.309-317
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• 1997

A sequential procedure for estimating a linear function of two normal means which satisfies the two requirements, i.e. one is a condition of coverage probability, the other is a condition of $\beta$-protection, is proposed when the variances are unknown and not necessarily equal. We give asymptotic behaviors of the proposed stopping time.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.101-113
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• 2002

In this paper we introduce a new score generating (unction for the rank regression in the linear regression model. The score function compares the $\gamma$'th and s\`th power of the tail probabilities of the underlying probability distribution. We show that the rank estimate asymptotically converges to a multivariate normal. further we derive the asymptotic Pitman relative efficiencies and the most efficient values of $\gamma$ and s under the symmetric distribution such as uniform, normal, cauchy and double exponential distributions and the asymmetric distribution such as exponential and lognormal distributions respectively.

• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.385-399
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• 2003

We first introduce the quasi-score estimating function and applied the quasi-score estimating function to nonlinear time series models. We proposed the M quasi-score estimating functions bounded functions for the quasi-score estimating functions. Also, we investigated the asymptotic properties of quasi-likelihood estimators and M quasi-likelihood estimators. Simulation results show that the M quasi-likelihood estimators work better than the least squares estimators under the heavy-tailed distributions

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.121-128
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• 2002

In this paper we provide a new proof of the asymptotic distributions of LAD estimators using the martingale limit theorem and show the efficiency of LAD estimators in a stationary AR(1) model setting.